3D MHD Equilibrium and Stability
For some decades there has been an international scientific and engineering program to study the containment of plasmas by toroidal magnetic fields with the aim of developing a fusion power reactor. Australia presently makes a major contribution to this program through the H-1NF Heliac which is a "stellarator" experiment located at ANU and is funded through the Major National Research Facility Program. Stellarators are an alternative to the better known "tokamak" types of experiments but have the great advantage of not needing large currents within the plasma in order to generate helical field lines. On the debit side, the lack of axial symmetry of stellarators makes their theory more complicated and simulation more computationally expensive than for tokamaks. In particular, the simply nested magnetic surfaces found in tokamaks can be broken and give rise to magnetic islands and regions of chaotic magnetic field lines. Present activities under this project are focussed on the area of 3D Resistive MHD Resistive Stability.
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Principal Investigator Henry GardnerTheoretical Physics, RSPhysSE Australian National University |
Project k12 |
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Co-Investigators David SingletonANU Supercomputer Facility Australian National University Bob Dewar Ben McMillan Theoretical Physics, RSPhysSE Australian National University |
RFCD Codes 240303 |
Significant Achievements, Anticipated Outcomes and Future Work
We have implemented a finite element model of the resistive MHD equations. As is typical of Finite Element Methods, the code ('Spector3D') consists of two main sections: 1) The calculation of the coupling between finite elements. 2) Solution of the dynamics: in this case we have a large matrix eigenvalue problem. We have continued the process of verification, and made several numerical and computational improvements to the code. Also, we have been able to analyse several cases of physical interest. In particular, we have examined three-dimensional effects inaccessible to other codes in order to determine the degree to which these effects are important. In addition, the code has been parallelised in order to access the high resolution test cases which are necessary to obtain accurate modelling of intrinsically three-dimensional effects. Debugging and development of the parallel code are still in progress.
Computational Techniques Used
The most significant performance issue is the solution of the large matrix eigenvalue problem. We have implemented the recently developed Jacobi-Davidson technique so that the Generalised non-Hermitian eigenproblem can be solved in ~N^2 time per eigensolution. The time-consuming operations of the technique are matrix by vector multiplications. We expect to perform a moderate (~1000) number of multiplications involving matrices with a large number (10**9) of nonzero elements. The code has recently been parallelised using MPI in order to access more memory and improve turnaround time. The computation of matrix elements is an intrinsically parallel task, but the eigenvalue solver requires a parallel matrix inverse solver. To this end we utilise the SCALAPACK library, which allows a scalable solution of the banded matrix inverse problem.
Publications, Awards and External Funding
External Funding and Awards
None.
Publications
B.F. McMillan, R.L. Dewar, R.G. Storer, Resolving the effects of toroidal and poloidal coupling on resistive modes in Heliotron E and LHD, Proceedings of the 14th International Stellarator Workshop (Greifswald, Germany, 2003)